I live about three hours away from Moab, and I used to go there often in my jeeps. Personally I think that earlier is good as a general rule. However I have seen people busting snow on some of the simpler trails because of going too early. It is a shame really, but there USED to be a jeep forum there in Moab, for people who lived in Moab. It was a wonderful resource to get online and find out the pulse of the area, weather, etc.
Anyhow I have also been told that later in the year is also a great time to get down there, but I have not managed it in all the time I have lived here. When it starts getting later in the year I am turning my attention to Ouray Colorado! (an amazing place if you have not been yet)
"Do you know what a soldier is...? He's the chap who makes it possible for civilized folk to despise war."